As a controlling device for railway electric cars, systems that drive and control an alternate-current motor by using an inverter have already been put into practical use. As is well known, accelerations and decelerations of railway cars are realized by powers that are transmitted between iron rails and iron wheels within the small contact areas therebetween. Thus, a controlling device for railway electric cars needs to control the torque of the electric motor in an appropriate manner so that the wheels do not spin free. In other words, if the torque is too high, the wheels spin free, and a friction coefficient (hereinafter, it may also be referred to as an “adhesion coefficient”) between the wheels and the rails decreases, so that the efficiency of transmitting the powers also decreases. As a result, problems arise where the railway electric cars cannot be accelerated in a satisfactory manner and where the wheels and the rails wear down. Conversely, if the torque is too low, although the wheels do not spin free, the railway electric cars cannot be accelerated in a satisfactory manner, and it becomes difficult for the railway electric cars to run on schedule. Also, the same applies to when a regenerative brake is used.
Conventionally, controlling devices for railway electric cars have a slip controlling system for inhibiting the slipping phenomenon of the wheels as described above. Generally speaking, such a slip controlling system is configured so as to determine a slipping state of the wheels by using rates of change of the wheels' speeds and a speed deviation among a plurality of wheels and to adjust the torque of the electric motor. There may be, however, some substances such as rain, snow, sand, and grease between the rails and the wheels. In addition, the adhesion coefficient greatly changes constantly according to the state of the surfaces of the rails and the wheels, the temperature, and the traveling speed of the railway electric cars. Thus, physical phenomena of the rails and the wheels are complex, and it is not easy to formulate a control law. For this reason, a large number of methods that can be used by slip controlling systems have been proposed based on theoretical studies from various aspects and data from test runs using actual railway electric cars (see, for example, Patent Document 1).    Patent Document 1: Japanese Patent Application Laid-open No. H06-335106